Acceleration Vector in Circular Motion

[mindarson]

Homework Statement

Consider a go-cart moving on a circular track of radius R = 40 m. Suppose it starts from rest and speeds up to 60 km/hr in 20 seconds, with a constant rate of increase of the speed.
Calculate the magnitude of a.

Homework Equations

a(t) = a_t + α

where the first term is the tangential acceleration and the second is the angular acceleration.

The Attempt at a Solution

I begin with the magnitude of a:

mag of a = [(R^2)(α^2) - (R^2)(ω^4)]^.5

Then I calculate ω:

ω = v/R = (60000m/3600s)/40m = .4167 /s

And I can calculate the tangential acceleration:

a_t = Δv/Δt = (60000m/3600s)/20s = .8333 m/s^2

Now I can calculate dω/dt = α:

α = r*a_t = 40 m * .8333 m/s^2 = 33.33 /s^2

Now to calculate the magnitude of the acceleration vector:

mag of a = [(a_t)^2 + α^2]^.5 = 33.34 m/s^2

But apparently this is wrong. Can anyone point out what I've missed? Seems pretty straightforward but I just can't get it.

 

[ehild]

Homework Statement

Consider a go-cart moving on a circular track of radius R = 40 m. Suppose it starts from rest and speeds up to 60 km/hr in 20 seconds, with a constant rate of increase of the speed.
Calculate the magnitude of a.

Homework Equations

a(t) = a_t + α

where the first term is the tangential acceleration and the second is the angular acceleration.
[/b]

Did you mean centripetal acceleration instead of angular one?

Now I can calculate dω/dt = α:
α = r*a_t = 40 m * .8333 m/s^2 = 33.33 /s^2

This is wrong. the tangential acceleration is R times the angular acceleration a_t=αR.ehild